German Offenlegungsschrift 38 39 297 discloses a device which guides the copied sheets output from a copier into a collecting station and collects them there in sets. The complete sheet stack is stapled and transported by a transport gripper from the collecting station to a depositing station, in which the sheet stacks are deposited one on top of another. For this purpose, the transport gripper transports the sheet stack until its end comes into contact against a fixed stop of the depositing station, opens its gripping jaws, and moves back to a point behind the fixed stop. Because the sheet stack is already, before the sheet stack is released by the transport gripper, resting with the majority of its surface area on the deposited stack located underneath, the end area grasped by the transport gripper and bent up by it may not necessarily drop into a flat position after it is released, since that area is elevated on the fixed stop. This elevated area causes the height of the deposited stack to increase more quickly, and thus reduces the depositing capacity. With this known device, the depositing capacity is additionally reduced by the fact that as is known, the deposited stack grows more quickly in the thicker stapled area. Both effects also cause an unstable stack structure, so that a precisely positioned stack structure is not guaranteed.